The electric conductivity is a material's ability of allowing the flow of electric current through itself. It is also defined as a natural property to measure the capacity of providing electrons (or electronic holes as is the case of semiconductors), ions or both types of particles or charge carriers that can flow through a material.
An electrolyte is a substance composed of ions; there exist different types of electrolytes such as liquids, solids and gases (plasma: highly ionized gas). Solid electrolytes can be made of a polymeric, ceramic and composite (polymeric-ceramic) material. A family of materials in constant growth is that of ionic solids, in which certain ions exhibit a quick transport. These materials are commonly named as fast ion conductors (FICs). In certain cases, the rapid transport of ions is accompanied by a considerable increase in electronic conduction (mixed conductivity).
There is a large interest in the science and technology of FIC due to their potential to be used as electrodes and electrolytes in conversion devices of electrochemical energy. These solid electrolytes have other applications in industry, including sensors to detect insulin and oxygen, the latter being used in automobiles. Other applications involve power systems such as electrochemical super-capacitors, fuel cells, batteries and accumulators such as those based on lithium.
In order for a solid to have fast ion conduction it must fulfill the following criteria [West A. R., Solid State Chemistry and Its Applications, John Wiley & Sons Essex, 1984]:                1. Have a high concentration of charge carriers or potential charge carriers.        2. Have a high concentration of vacancies for ion movement or interstitial sites.        3. Have a low activation energy for ion movement.        4. Have the presence of a set of energetically equivalent sites partially occupied by other mobile ions.        
FICs are not a new discovery. In 1914, Tubandt and Lorenz observed this behavior in certain silver compounds. These researchers discovered, for example, that ionic conductivity of AgI before fusion was approximately 20% higher than that of the melted solid. The FICs were also observed in other two iodine compounds and AgSI. As it was mentioned in FICs one of the groups of ions, cations or anions is free to move. That group is called sub-reticle and generally it is in a melted state. That model was proposed by Strok in 1936 based on structural and thermodynamic data of AgI. In most of the FICs, entropy for transition to the FIC state is higher than that of a non-conducting FIC. For example, in the AgI, the transition entropy from form b (non-conducting) to a (fast conducting) form at 420 K is 14.7 JK−1mol−1, while the fusion entropy at 861 K is hardly of 11 JK−1mol−1.
The special electric properties of α-AgI led to an unavoidable search for other solids that exhibited a high ionic conductivity, mainly at temperatures lower than 420 K. The most successful solid at present, despite the existence of others, involved the partial change of silver by rubidium to form an RbAg4I5 compound. This compound has an ionic conductivity of 2,500 Sm−1 at room temperature, which is higher than that of a NaCl sodium that has an activation energy of just 0.07 eV (1.12×10−20 J). The crystalline structure is different from that of α-AgI, but similarly, the ions of Rb+ and I− form a rigid reticle, while those of Ag+ are randomly distributed in a grid of tetrahedral sites in which they can move [Smart, L.; Moore, E., Solid State Chemistry: An Introduction. Chapman & Hall, Londres, 1993].
To be useful as a solid electrolyte in a battery, an ionic conductor not only must have a high electrical conductivity but also negligible electronic conductivity to avoid the battery short circuiting. Electrons have to cross the external circuit where they can be used to make a useful work. The electronic conductivity of RbAg4I5 is considerably small (10−7 Sm−1) so that it has been used as a solid electrolyte in batteries with electrodes made of Ag and Rbl2. Such cells operate in a wide range of temperatures 217-473 K (−55 to 220° C.), require a long time to store energy and provide a high mechanical resistance.
The most promising application of FICs is in solid state batteries, where two types of batteries exist:                1. Small primary cells; they must have a long lasting life and must not be discharged during this period        2. Rechargeable secondary batteries; they are used when a high density of energy is the selection criterion.        
The batteries of the first type find application as miniature cells; they operate at room temperature and have a long lasting life in the order of years instead of a high density of energy or a high outlet voltage. They are used in watch clocks and photographic machines, pacemaker and military applications. The secondary batteries manage a lithium anode, lithium iodine as electrolyte and the complex as cathode:Anode(Li): 2Li(s)2Li++2 electrons  Equation (1)Cathode(I2): I2(s)+2 electrons2I−  Equation (2)Total: 2Li(s)+I2(s)2LiI  Equation (3)
As LiI has vacancies in the reticle and as a result of the small size of Li+ cations, these are able to migrate through the solid electrolyte whereas electrons flow through the circuit.
There are several devices and equipment suitable to measure the conductivity of solid electrolytes but most of them have their application in liquid solutions. For solid systems, devices based on the Van der Pauw's method are used (FIG. 1).
Other equipment in use for the measurement of resistivity is that of Van der Pauw, in which the sample used can have an arbitrary form (though homogeneous in composition and thickness) and electric contacts can be taken on any point of its profile. The only restriction is that the sample must be thin. FIG. 2 shows a diagram corresponding to the setup of equipment.
At first, the potential difference between C and D, VCD=VD−VC is measured by passing an electric current between A and B to calculate R1:R1=VCD/IAB  Equation (4)
The voltage difference between A and D, VDA=VA−VD is measured by passing an electric current between B and C to calculate R2:R2=VAD/IBC  Equation (5)
In agreement with Van der Pauw's method, resistivity ρ is given by the expression:
                    ρ        ≈                                            π              *              d                                      Ln              ⁡                              (                2                )                                              *                                                    R                1                            +                              R                2                                      2                                              Equation        ⁢                                  ⁢                  (          6          )                    
where d is the sample thickness.                R1 is the vertical resistance        R2 is the horizontal resistance        
When resistivity measurements are performed on samples with a form of rectangular parallelogram, the four point method is used (FIG. 2). Current is introduced in two parallel faces of the sample, whilst voltage is measured in two intermediate points within this distance, thereby avoiding a voltage loss in the points of electric contact (impedance at voltmeter entrance must be much higher than that of the resistance between voltage contacts).
A sample resistivity is given by expression:ρ=VA/IL  Equation (7)where V is the voltage, I is the current, A is the sample section and L is the distance between the voltage contacts:
Nevertheless, the specific determination of ionic carrier is not identified by means of this equipment so that the application of blocking or selective electrodes (that permit the pass of electrons or ions only) is widely useful in determining carrier type (For example, if a solid electrolyte transports two types of ion carriers such as “A” and “B” then it is possible to have electrodes that permit only the pass of “A” or “B” ion to be determined but not both at the same time).
With the aim of having a cell that measures not only the general electric resistance but also a specific resistivity (or conductivity), it is possible to know from it what type of carrier is having effect on work. The present conductivity cell has been therefore developed with blocking and selective electrodes.
In the reference J. Phys. Chem. 1991, 95, 6040-6044, an open cell is shown in a two-electrode set up with charge carriers that flow on the surface. In this cell, it is not possible to control pressure and relative humidity of input gas to the system, so that membrane was hydrated before placing it in the conductivity cell to obtain values by means of electrochemical impedance.
In the reference Electrochimica Acta 48 (2003) 4175-4187, the Van der Pauw's method of four electrodes is used, in which iterations were carried out on equations to obtain a conductivity value, likewise charge carriers flow on the membrane surface.
In US 2010/0109651 A1, a conductivity cell can work with two or four electrodes, but only with one atmosphere, and conductivity measurement is performed on surface and not through it.
U.S. Pat. No. 4,118,549 describes a solid state cell to measure conductivity of the battery type composed of two electrodes, which does not permit gas entrance. Electric charge transportation is through membrane but it does not have a heating system or pressure control.
In U.S. Pat. No. 4,871,427, the cell described consists of two electrodes, which can handle liquids only but not gases.
In U.S. Pat. No. 6,228,325, a cell to measure the quantity of carbon by means of electric conductivity is reported. Despite having generally the same principle of operation as the invention cell, this application is different and more specific for this case.